Question 74693This question is from textbook Elementary Statistics
: In a recent survey, 66% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 11 of them favor the building of the police substation.
This question is from textbook Elementary Statistics
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! In a recent survey, 66% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 11 of them favor the building of the police substation.
:
This is a binomial probability problem.
The formula for that is:
 for x=0,1,2,...,n
Where:
n=number of trials
x=number of successes among n trials
p=probability of success in any one trial
q=probability of failure in any one trial (q=1-p)
:
! is a factorial symbol that denotes the product of descending numbers, like this:
4!=4*3*2*1 If your in a statistics class you probably have a calculator with the ! symbol available some where. For the TI 83 to TI 84, hit [MATH] arrow right>>> to PRB it's 4:!.
:
Some teachers allow you to shorten the formula to:
P(x)=[n]C[r]*p^x*q^(n-x)
r=x=number of successes among n trials.
All of the other symbols are the same as the first formula. If you're one of those, then you should know how to do it with your calculator.
:
I'm going to show you with the first formula.
p=66/100=.66
q=1-p=1-.66=.34
n=14
x=11
Round to whatever your teacher wants, most don't require more than 4 decimal spots.
:
I don't know how much work your teacher needs to see. If they only want an answer, then....
If you have a TI 83 to TI 84, these can be done by following these steps:
[2nd] [VARS] arrow down to 0:binompdf [ENTER]
type in [n] [,] [p] [,] [x] [)] [ENTER]
In this case it will look like binompdf(14,.66,11)=.1480885312
:
Look the instructions up for the calculator that you're using if it's not a TI 83 or 84.
Happy Calculating!!!!
|
|
|
